What did Anna mean at the end of "uninvited"? I don't quite understand, and what's written on the door?

It's that man's name, Kemp. As for the sentence "Anna always wanted to kill her stepmother (the film finally tells us that her mother and sister died because she wanted to burn her stepmother", the therapist said before that she should move on with her life when she was told to finish everything, but Anna understood that the therapist supported her to kill her stepmother! But she seems to have been cured, as if forgetting that she wanted to kill her stepmother before! So, she began to imagine that the dead Alex appeared, as well as her mother and those children. All this happened very strangely, so she naturally "speculated" that her stepmother was a perverted murderer (that is, the woman opposite her ward was the real material of her imagination), which gave her motive to kill her stepmother, so she finally started to do it! Anyway, Anna killed her mother and sister. She chose to escape and put the blame on her annoying stepmother. In her imaginary world, her stepmother became a murderer, so she killed to save her family.